ster was right: the strict severity of our approaching
examination allowed of no such dreamer's outbursts. Was I, on my side,
very wrong? To warm chill calculation by the fire of the ideal, to
lift one's thought above mere formulae, to brighten the caverns of
the abstract with a spark of life: was this not to ease the effort
of penetrating the unknown? Where my comrade plodded on, scorning my
viaticum, I performed a journey of pleasure. If I had to lean on the
rude staff of algebra, I had for my guide that voice within me, urging
me to lofty flights. Study became a joy.

It became still more interesting when, after the angularities of a
combination of straight lines, I learnt to portray the graces of a
curve. How many properties were there of which the compass knew nothing,
how many cunning laws lay contained in embryo within an equation, the
mysterious nut which must be artistically cracked to extract the rich
kernel, the theorem! Take this or that term, place the + sign before it
and forthwith you have the ellipse, the trajectory of the planets,
with its two friendly foci, transmitting pairs of vectors whose sum
is constant; substitute the--sign and you have the hyperbola with
the antagonistic foci, the desperate curve that dives into space with
infinite tentacles, approaching nearer and nearer to straight lines, the
asymptotes, but never succeeding in meeting them. Suppress that term and
you have the parabola, which vainly seeks in infinity its lost second
focus; you have the trajectory of the bombshell; you have the path of
certain comets which come one day to visit our sun and then flee to
depths whence they never return. Is it not wonderful thus to formulate
the orbit of the worlds? I thought so then and I think so still.

After fifteen months of this exercise, we went up together for our
examination at Montpellier; and both of us received our degrees as
bachelors of mathematical science. My companion was a wreck: I, on the
other hand, had refreshed myself with analytical geometry.

Utterly worn out by his course of conic sections, my chum declares that
he has had enough. In vain I hold out the glittering prospect of a new
degree, that of licentiate of mathematical science, which would lead
us to the splendors of the higher mathematics and initiate us into the
mechanics of the heavens: I cannot prevail upon him, cannot make him
share my audacity. He calls it a mad scheme, which will exhaust us and
come to nothin